| Title:
|
Closed semistable operators and singular differential equations (English) |
| Author:
|
Koliha, J. J. |
| Author:
|
Tran, Trung Dinh |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
605-620 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study a class of closed linear operators on a Banach space whose nonzero spectrum lies in the open left half plane, and for which $0$ is at most a simple pole of the operator resolvent. Our spectral theory based methods enable us to give a simple proof of the characterization of $C_0$-semigroups of bounded linear operators with asynchronous exponential growth, and recover results of Thieme, Webb and van Neerven. The results are applied to the study of the asymptotic behavior of the solutions to a singularly perturbed differential equation in a Banach space. (English) |
| Keyword:
|
closed linear operator |
| Keyword:
|
$C_0$-semigroup |
| Keyword:
|
infinitesimal generator |
| Keyword:
|
semistable operator |
| Keyword:
|
singular differential equation |
| MSC:
|
34G10 |
| MSC:
|
47A10 |
| MSC:
|
47A60 |
| MSC:
|
47D06 |
| idZBL:
|
Zbl 1080.47500 |
| idMR:
|
MR2000056 |
| . |
| Date available:
|
2009-09-24T11:04:54Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127826 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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